Optical systems in which parallax is eliminated



March 13, 1962 G. w. HAMSTEAD 3,024,698

OPTICAL SYSTEMS IN WHICH PARALLAX IS ELIMINATED Filed Jan. 20, 1958 N Nk, my. N. r y ww f Q m m 2V m NNNE NT f WQ M l@ AKNWW DMN A N am Nw w /AQ .Kw

/f/ A w ,M .A Q- .9 y rwbu @QI l @si S3 Y usbbhs! ha- \`Ql .Qs i \\%h AN n .Alsw ws- NS .....Il vm nw mwmm- I 1 NQJ. hib .TQ #s m. w d@ .a wb.. mu mi 3,024,698 OPTICAL SYSTEMS IN WHICH PARALL IS ELIMINATED George William Hamstead, Barnet, England, assigner to v W. Watson Sons Limited, Barnet, Hertfordshire, England, n company of Great Britain Filed Jan. 20, 1958, Ser. No. 710,090 Claims priority, application Great Britain Jan. 23, 1957 4 Claims. (Cl. 88-57) The invention relates to optical systems and is more particularly concerned optical image producing systems for focussing nays to form an image of an object. Owing to aberrations and other imperfections, practical image producing systems do not form a perfect image of an object. In particular, the position on the axis at which rays are brought to a focus varies with the fractional aperture of the zone of the exit pupil through which the rays pass.

It is an object of the invention to provide an improved optical image producing system.

The invention provides an optical image producing i system having the best focus for definition coincident with the focus at'which parallax is eliminated or at a The invention also provides an optical image producing system which satisfies the condition that rays considered to pass, according to the laws of optics, through the zone of the exit pupil having a fractional aperture f substantially are brought by the system to theparaxial focus thereof. If the exit pupil is defined by the stop, and could be increased by removal of the stop to expose the said zone,

then on such removal the said rays passing through that zone to the said focus would exist; otherwise the said rays do not exist but their path can be constructed or calculated.

The invention also provides an optical image producing system which satisfies the condition that rays which pass through the zone of the exit pupil having a fractional aperture of substantially one (i.e. marginal rays) are brought by the system to a focus on the axis thereof which focus (referred 4to as the marginal focus) is distant from the paraxial focus by substantially $6 of the distance betweentheparaxialfocusandthefocusontheaxistc which rays which pass through the zone of the exit pupil having a fractional aperture substantially are brought by the system.

The invention now be further described with reference to the accompanying drawings, in which:

FIGURE 1 is a diagram showing a wave-front which has emerged from the exit pupil of an optical image producing system,

`FIGURES 2 and 3 are graphs of some mathematical expressions referred to in the description, and

FlGURE4isadagramofaspeciticoptical system embodying the invention.

In FIGURE 1, O is a selected focal position on the axis AO of the system; that is to say an surface or a graticule or the like intercepts the axis at O or is conjugate therewith, or an eyepiece is focussed on to O. AE represents the plane of the exit Pupil, APQ is the section of the reference sphere centred on 0, ARS is the section of the wave-front, RM is a ray, defined as a normal to the wave-front, RO is the normal to the reference sphere and is the ideal direction of RM.

ICC

. 2 Ilhe angular aberration i' (psi) is measured by the angle MRO. RT is drawn as an arc of a circle centred on 0 to cut Q0 at T.

iIf the angle AR=0 and the angle RS=M (-i.e. a small increase in 0), then considering the triangle RSI, when 60 is small -it is seen that:

angle SRL-:angle Ml0=\lt and TS t3!) The wave-front 'aberration W, at 0, is defined as W=N.PR= [PR] the medium having a refractive index N. At 0+ the wave-front aberration becomes W-HW so W+aW= [QS] =IQT1 [TS] Obviously PR=QT to [PR]=[QT] and therefore 6W=[TS] so that ProvidedthatWsverymuchlessthanAOitisseenthat, very nearly,

RT=PQ and PN=PQ cos 0 with PN=UV For small aberrations tan \I \If and cos 0 may be taken as unity (for a focus at infinity cos 0:1) and conse-- quently:

1 dW twv?? The axial spherical aberration with respect to the paraxial focus may be represented by a two term formula. Denoting Wp as the wave-front aberration with respect to the par-axial focus:

met-:starrt where the coetlicients a, and a, conventionally represent the primary and secondary spherical aberration of the system respectively.

lftheselectedfosoisnottheparaxialfocusthena p 2 12(PO) lproportional to the square of the fractional aperture has to be added u w, a, being a fader dependent upon the distance of O from the paraxial focus.

Patented Mar. 13, 1962 vtr-@afm The criterion of the denition, D, of an optical system is taken as:

and:

I is the intensity at the centre of the ditraction image that the system produces of an idea-l point object, I is the intensity in the ideal case of the system being free from aberration, A is the wave-length of the light, and E0 is where W is the wave-front aberration above referred to. and V is the square of the fractional aperture, i.e.

hier l'he above criterion of the denition is valid provided that the definition approximates to the suo-called Raylei@ limit, that is to say D is not less than 0.8. When D=0.8

ForDtobeatmaximum,Bmustbeataminimum. For the above quoted expression, for B0 to be at a min imum,

0z= 0+1900| For zero parallax at the edge of the exit pupil:

33 mama For D to be not less than 0.8 it follows that [al is not greater than 1.5O62\I if has zeros at Theturningvaluesof'areat o= iossresz and iososse 4 with corresponding values of a 0.456763? and i 0.513617g; respectively FIGURE 2 shows the last quoted expression for W, expressed in units of as. FIGURE 3 shows the last quoted expression for I expressed in units of For the aforementioned limiting value for Ial=1.5062 and an objective of 25 mm. clear aperture the larger zonal value of lf is about 7 seconds of arc. Iasi is Ilimited to about M5 per second of arc of parallax. If we measure I with respect to the paraxial focus:

*2 Y @l 'pn-.gi f3-(Po +6 m For zero longitudinal spherical aberration `If=zero and this is so if '=0 or er# Pu pu 5 Taking the latter case the required design criterion is that the ray passing through the zone of fractional aperture (numerical value=l.183216) is brought to the paraxial focus.

where LA=longitudinal spherical aberration at a paraxial angle u, with respect to the selected focal position O. Now if u., is the maximum paraxial angle:

From the expression forl W quoted earlier, it follows that s 1 2 Q n LA-alui 5 ,ma lg-QGY (2)1 @is 5 p +6 p0 Thus LA=0 when p=p i.e. the selected focus is the marginal focus. (This follows since im has been assumed to be zero.) With respect to the paraxial focus:

and for the marginal (o1 rim) rays p=po, so

sptes@ For the zonal rays for which Comparing those two expressions, it follows that LA=%LAz is equivalent to the condition that the rays through the zone are brought to the paraxial focus.

'Ihe specilc optical system shown diagrammatically in FIGURE 4 will now be descnibed by way of example.

The system of this example is a sighting telescope for use in setting the sights of guns. The system, in use, is inserted in the muule of a gun so that the axis of the objective 11, 12 is aligned with the axis of the muzzle end of the bore of the gun. Light 20 from an object at an effectively infinite distance passes through the objective and through a prism system, the length and entrance and exi-t face r4, rS, are represented diagrammatically by the rectangle 13. The prism system 13 merely changes the direction of the axis of the light beam so that it is taken to an eyepiece 21 at an accessible position outside of the gun bore. The marginal rays of the light 20 are brought to a focus at Fm which is the marginal focus of the system 11, 12, 13. A graticule having a fiducial mark, e.g. in the form of a small dot or crosslines, is positioned at Fm. 'Ihe focus Fm is 0.098 mm. (all dimensions hereinafter referred to are also in mm.) to the left of the paraxial focus Fp, which is 28.533 to the right of the surface rS. A ray through the zone of the exit pupil having a fractional aperture of V2 is brought to a focus at a distance of 0.110 to the left of the paraxial focus.

The eyepiece 21 is focussed on to the marginal focus Fm and the graticule so that a parallel beam of light 22 emerges from the eyepiece. The joint image of the infinite object and the iiducial mark seen in the eyepiece has substantially no parallax and the maximum definition obtainable with the system. The graticule is positioned 5.505 to the left ofthe surface r6.

The shapes, sizes, relative positions and refractive indices of the components of the system are given in the following table:

passing Component Axial dis- Refractive Clear diamor lens element Surface tance (d in index of eter (D 1n and air radii in mm. mm.) beoomponmm.) of comspacings tween ents ponents and surfaces elements 11 dl l. M3 Dill t 12 iis-3.0 1. 626 D128.0

Air d;5.0.--..-- Y

rlw Air d|33.94...--

14 dts-1.0 1. 708 D;14.3

Air 1n-2.3

Air dja-0.9

17 dlr-3.5 1. m D|12.4

18 diz-1.0 1. 626 D-12.4

The value of a, for the system 1l, 12, 13 is approximately 1.321; the larger zonal value of p (i.e. the larger maxima in FIGURE 3) is only about 5% seconds of arc and the smaller zonal value of :p (i.e. the smaller maxima in FIGURE 3) is only about 5 'seconds of arc.

The equivalent focal length of the objective l1, 12 is f about and the equivalent focal length of the eyepiece 21 is about 15. The telescope thus has a magnification of 7 times and an exit pupil diameter of 4.

The eyepiece 21 is corrected to a residual spherical aberration of M8 (equallto half the so-celled Rayleigh limit). It is corrected for coma and has a ilat field when used in conjunction with the rest of the system.

The invention is not restricted to the details of the foregoing example. For instance, the distance between the surfaces r3 and r4 may be increased to 33.435 in which case the marginal focus falls at the surface rS and the graticule may be placed on that curface, or on a cover plate cemented to that surface, the eyepiece being moved to focus on to it. t

I claim:

1. An optical image producing system having spherical aberration and comprising refracting surfaces distributed along an optical axis, wherein the radii of the said surfaces, the axial distances between the said surfaces, the refractive indices of the media-between the said surfaces and the apertures of the said surfaces, are selected so that rays which pass through the zone-of the exit pupil having a fractional aperture of substantially one are brought by the system to a marginal focus on the axis, which marginal focus is between the object and the paraxial focus and is distant from the paraxial focus by substantially 6 of the distance between the paraxial focus and the focus' on the axis to which rays which pass through the zone of the exit pupil having a fractional aperture substantially l .V2 are brought by the system, whereby the best focus for definition is coincident with the focus at which parallax is eliminated or at a minimum.

2. An optical image pioducing system as claimed in claim 1, including an eyepiece focussed on to the said marginal focus.

3. An optical image producing system having spherical aberration and comprising optical surfaces distributed along an optical axis, wherein the radii of the said surfaces, the axial distances between the said surfaces, the refractive indices of the media between the said surfaces and the apertures of the said surfaces, are selected so that rays which pass through the zone of the exit pupil having a fractional aperture of substantially one are brought by the system to a marginal focus on the axis, which marginal focus is between the object and the paraxial focus and is distant from the paraxial focus by substantially of the distance between the paraxial focus and the focus on the axis to which rays which pass through the zone of the exit pupil having a fractional aperture substantially V2 are brought by the system, whereby the best focus for definition is coincident with the focus at which parallax is eliminated or at a 4. AnL optical image producing system as claimed in claim 3, including an eyepiece focussed on to the said marginal focus.

References Cited in the tile of this patent UNITED STATES PATENTS 2,398,276 Altman Apr. 9, 1946 2,441,036 Schade May. 4, 1948 2,500,017 Altman Mar. 7, 1950 2,559,881 Kingslake et al. July 10, 1951 2,784,645 Grey Mar. 12, 1957 (Other references on following page) 2,899,862 Baker Aug. 18. 1959 Th P 1 i 0 ti b A C H d d'F H 5 e rlnclpeso pcs, y aryan FOREIGN PATENTS Perrin, 1st Edition, published in 1932, by McGraw-Hill 608,586 Great Britain Scpt. 17. 1948 Book Co., Inc., New York, N.Y., pages 68-79. 

